The cosine function is a periodic function which is very important in trigonometry.
The simplest way to understand the cosine function is to use the unit circle. For a given angle measure , draw a unit circle on the coordinate plane and draw the angle centered at the origin, with one side as the positive -axis. The -coordinate of the point where the other side of the angle intersects the circle is , and the -coordinate is .
Once you know these values, you can derive many other values for the cosine function. Remember that cos\theta; is positive in quadrants and and negative in quadrants and .
You can plot these points on a coordinate plane to show part of the cosine function, the part between and .
For values of less than or greater than you can find the value of using the reference angle .
The graph of the function over a wider interval is shown below.
Note that the of the function is the whole real line, while the range is .
The period of is . That is, the shape of the curve repeats every -unit interval on the -axis.
The amplitude of is , that is, the height of the wave.
The modified function has amplitude and period / .